The real way to make people rely less on the ability to load (because that actually is, what safe restrictions really seem to try to achieve), is to make failure recoverable without loading. There is no point in saving if you know for sure, that you won't want to load that save. TDM is one of the most stable games today. People almost only save for reallife reasons and to insure against ingame failure (either in general every N minutes or before trying something expected to be a gamble - like extinguishing a torch using a water arrow).
Designing for absolute recoverability is at least pretty damn hard. But having safe spaces (rooms, the AI can't reach) near difficulty spikes, reducing the AI cooldown time and using a clear design language would probably make people feel less in need of that revorey insurance already. Important would be to actually advertise deviations from the standard path - so players know, how this mission is different.
As an example, expecting the player to get that in your mission headshots kill zombies is a bit far a stretch when the player has played literally over a hundred other missions where headshots wheren't killing zombies. Such stuff would need explicit advertising because a lot of players would only be able to get that insight by accident or reading the spoilers in a forum thread otherwise.
Death actually is the elephant in the room. The biggest ingame failure, players insure against by saving, is the death of the player's avatar. So that would have to be eliminated somehow. Technically, it doesn't actually exist right now either as the player can just reload. But that mechanic obviously needs to be replaced by something else if you want players to be confident that they won't want to load. Waking up in a cell instead of dying, just spawning in a nearby safe room, being left for dead but recovering a bit after the AI leaves the scene - all potential replacements for one or the other situation normally undone by a quick tap on the quickload key. There should be way more possible ways to replace that final game element (i just am not that creative). But the point is, that there needs to be a non-final replacement for that final ingame failure.
And then there are other ways of getting stuck - on geometry, by going somewhere the designer didn't thought to be accessible, killing the wrong person or just by accidently throwing a key into an inaccessible gutter. These aren't that common (well, the first one is, but the noclip console command exists). But players, who don't save regularly, start doing so when experiencing a non-recoverable situation. So these situations have to be made hard to create or otherwise catered for.
On the extreme end, it may be possible to create missions that exhibit no reason for saving apart from meatspace stuff like having to go to sleep. But you aren't fully against saves. So just having a sane autosave system can already do a lot to make the player save less. When the player enters a safe room and ther wasn't just an autosave - just perform an autosave. It signals the player, that this indeed is a safe room - and that you took care of his insurance already.
If going the path of confidence, i would actually advice against using save items or manually activatable "bonfires". If the player thinks about saving, they will do so and just fall back to the (still available) save system, they have been trained use by all the games and missions that came before yours.
TLDR: If you really want players to not save, give them the confidence that they won't want to load.